thermal field in a nmr cryostat - comsol multiphysics · thermal field in a nmr cryostat . overall...
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Annunziata D’Orazio
Agostini Chiara
Simone Fiacco
Thermal Field in a NMR Cryostat
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Overall Objective of Research
Program
The main objective of the present work was to study thethermal field inside the cryostat:
1) developing three different models of cryostat withparticular reference to the type of closures placed at theends.
2) considering insulation and boundary conditions able tosimulate the effect of a "cold head" placed in contact witha very limited portion of the cryo-shields.
3) considering tie - rods mounted in real cryostat to maintainthe empty cavity and to center the magnetic field.
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OUTLINE
Introduction
Modelling Using Comsol Multiphysics
Results
Conclusions
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NMR Superconducting Magnet
Advantages
Homogeneous, stable and high static field
Possibility to disable the power to the magnet
Excellent diagnostic image
Disadvantages
Expensive
High residual external field (require shielding)
Maintaining cryogenic temperatures
Quench risk
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Structure of cryostat
Concentric structure
coaxial with the
superconducting windings
to avoid helium
evaporation
Composed by:
Magnet immersed in
liquid helium at 4 K
Radiative shields
Cold headFigure 1: Cryostat’s scheme with
cryo-shields and cold head
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Real Cryostat
Figure 2: Front view of a real cryostat Figure 3: Concetric vessels
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Simplified geometry of Cryostat
At the beginning a very simplified model ofcryostat constited of open concentric cylinders spaced from vacuum zones hasbeen developed.
This model no take into account the thermalfield near the closures simulating only the heat exchange in the central part of the cryostat.
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He 4,2KExt. steel vessel 0,625cm
Ext. Aluminum shield 0,40cm
20K
Int. Aluminum shield 0,61cm 80K
Int. steel vessel 0,45 cm
Vacuum is made between the shields
First shell
Second shell
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Model of Cryostat with closures
A more realistic model has been developed to
investigate the thermal field near the closures.
More specifically, three different geometries with
particular reference to the type of closures placed
at the ends have been implemented.
Geometry with flat closures Geometry with inclined
closures
Geometry with rounded
closures
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Mesh
Swept mesh with
elements of different
sizes :
Closures:
Maximum element
size 0.1 m
Cylinders:
Maximum element
size: 0.2 m
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Materials
Type of
material
ρ
(kg/m3 )
Thermal
conductivity
[W/m K]
Specific
Heat
[J/K. kg]
Outer
vessel
304
Stainless
Steel
7999.5 Variable with
Temperature
Variable with
Temperature
Radiative
Shields
6063 – T5
Aluminum
2712.6 Variable with
Temperature
Variable with
Temperature
Inner
vessel
304
Stainless
Steel
7999.5 Variable with
Temperature
Variable with
Temperature
Cold head OFHC
Copper
8940 Variable with
Temperature
Variable with
Temperature
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𝜌𝐶𝑝𝜕𝑇
𝜕𝑡+ 𝜌𝐶𝑝𝐮 ∙ 𝛻𝑇 = 𝛻 ∙ 𝑘𝛻𝑇 + 𝑄
Change in
internal energy
in the domain
Convective
term
Conductive
term
Heat Source
Boundary condition
Heat flux
Radiation Surface to ambient;
Radiation Surface to Surface
Specified temperature
Specified inward heat flux
Initial conditions:
External Temperature=293.15 K
Internal temeperature: 4.2 K
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Heat convective transfer coefficients (1)
Helium Liquid
Vapor
Air External
cylinder
Internalcylinder
Vertical wall
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External steel vessel
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Internal steel vessel
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DAM (Double
Aluminized Mylar)
Mylar
Higher temperature
gradient region
Aluminum
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Simulation without DAM
The radiative net heat flux received by the shield maintained at 80K is very high
and not sustainable by any commercial cold head
Thermal Boundary
conditions:
Specified temperature on
raditive cryo-shields
maintained at 80 K and 20
K respectively.
External vessel
Internal vessel
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Simulation with DAM (1)
External steel
DAM
Ideal case:
separated DAM sheets: no
contact points are considerated
(only radiation between sheets)
a single sheet with an
effective emissivity taking in
account the effect of 60 DAM
sheets
Perfect insulation
The heat flux entering the external aluminum vessel, from
698.42 to 2.985 W.
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Simulation with DAM (2)
SPACER
(10um)
DAM(10um)
A more realistic model was analyzed in Matlab
• In addition to the radiative contribution, a further
conductive term was considered throught the
spacer (k=0.0012)
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Cold Head
In combination with an effective insulation
system, radiative shields are maintained at a
specified temperature by a “cold head”.
In this work the Pulse Tube Refrigerator with
two refrigerating stages is used in order to
reduce the temperature gradient in the cryostat.
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Model of Cold head in Comsol
TF80
• rTF80=20.6 mm
• sTF80=5 mm
TF20
• rTF20=10.3 mm
• sTF20=4 mm
Alumimun
shield at 80 K
Two copper plates
(4.12 cm diameter
and 2.06 cm
diameter),
simulating two
refrigerant stages of
a pulse tube, put in
contact with two
cryo-shields
Thermal boundary
conditions :
Specified temperature
Specified inward
heat flux
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Boundary Condition
The imposed heat flux, to be removed by the refrigerating
stage through each contact surface, was set as equal to the
overall difference between the incoming and outgoing flux
from the shield
QTF80
QTF20
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Geometry with flat closures
Thermal performance (1)
External
Aluminum
shield
Internal
Aluminum
shield
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Thermal performance (2)
Imposed temperature at the
cold head surfaces
Internal
Aluminum
shield
External
Aluminum
shield
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Zero-Boil Off System
Condensation inside
the vessel of helium
that could be
evaporated, eliminating
helium consumption.
Single shield
Two refrigerate stages
(50 e 4,2 K)
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Model of Cryostat
Geometry with three vessels
Thermal Problem
Statement:
• T50
• T4.2
• E_dam=0.00133
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Results with cold head
Aluminum
shield
Helium
vessel
The temperature below
4.2K allows the helium
vapor recondensation
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Simulation with tie rods
For MRI machines, tie-rods are made of fiber glass
because this material achieves a mechanical
resistance near to theoretical resistance of the
covalent bond.
Each vessel contains 4 tie-rods which fix it on the
opposite one.
Provide a conductive way for heat among the
vessels.
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Temperature fields along tie rods
for imposed heat flux (1)
Thermal field along fiber glass tie-rod
inserted between esxternal and internal
aluminum vessel
Temperature field along fiber glass
tie-rod in contact with internal steel
vessel containing liquid helium
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Temperature fields along tie rods
for imposed heat flux (2)
Thermal field on External
Aluminum Vessel
Thermal field on External
Steel Vessel
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Discussion
Temperature value at the end of the tie-rod, in
contact with the external steel, is lower than
the average temperature of the vessel (equal to
293.1 K).
For internal steel vessel this effect is not
negligible since the temperature value at the
contact points with tie-rods reaches a value of
5.79 K so the liquid helium evaporates very
quickly
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Conclusions (1)
Preliminary results related to the description of
thermal field in a cryostat for nuclear magnetic
resonance imaging have been presented.
Resulting heat flux entering in 80K cryo-shield
without DAM’s sheet is too high and not
sustainable by any commercial cold head.
Two boundary conditions have been analyzed to
simulate the effect of the cold head.
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Conclusions (2)
Zero-boil off system have been simulated with
helium vessel maintained at 4K; resulting heat flux
entering in cryo-shield and vessel wall is
sustainable by cold head.
With regard to tie rods, the choice of material is
crucial to maintain the empty cavity and avoid the
quench of magnet.
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FUTURE DEVELOPMENTS
Next simulations will concern
more realistic geometrical and
mechanical configurations.
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Acknowledgments
The authors thank Prof. Francesco Paolo
Branca for constructive comments and
helpful suggestions and for making available
the NMR tomography.